Vertical relations

David Ettinger (thanks Marc Bourreau)

Paris-Dauphine, PSL

Marc Bourreau adapted (TPT) Vertical relations 1 / 56

Structure

1 Vertical relations and vertical restraints.

2 The double-marginalization problem.
3 Remedies to the double-marginalization problem
Vertical integration.
Two-part tariff.
Fixing a maximal price.
An example.
4 The free-rider problem.
5 Remedies to the free-rider problem
Exclusive territorial agreements.
“Resale price maintenance” contracts.
An example.
6 Competition between suppliers.
7 Vertical restraints and public policy.
8 Vertical Oligopoly and vertical mergers

Marc Bourreau adapted (TPT) Vertical relations 2 / 56

 Vertical relations and vertical restraints

Vertical relations

Definition of vertical relations

Relationships between two firms in the sequence along the value chain (rela-
tionships such as client-supplier relation)

Vertical relation , “horizontal” relations between firms at the same level of a

value chain (competition, horizontal mergers, ...).

Value chain
Set of production activities that brings the raw materials to a finished product.

Marc Bourreau adapted (TPT) Vertical relations 3 / 56

 Vertical relations and vertical restraints

Vertical relations

Vertical relations , Supply-demand relations (choice of consumers, pricing

decisions, ...).

Many firms sell to other firms, not (only) to final consumers.

A cement producer sells its cement to construction firms...
A TV manufacturer sells its products to retailers...
A manufacturer of telecom equipments sells its products to telecom oper-
ators...
... which in turn sell their products to final consumers (or to other firms).

Marc Bourreau adapted (TPT) Vertical relations 4 / 56

 Vertical relations and vertical restraints

Vertical relations

The specificities of B2B as compared to B2C

Marc Bourreau adapted (TPT) Vertical relations 5 / 56

 Vertical relations and vertical restraints

Vertical relations

The specificities of B2B as compared to B2C

A firm that sells to final consumers controls most of the variables that
impact the demand (price, quality...), which is not the case of firms selling
to other firms.
Client firms can compete with each other, which cannot be the case for
final consumers.
The number of client firms can be lower than the number of final con-
sumers. It may even be the case that the client firm has more power than
the provider (Monopsony).

Marc Bourreau adapted (TPT) Vertical relations 5 / 56

 Vertical relations and vertical restraints

Vertical relations

In order to simplify the analysis, we usually consider only two levels.

Upstream firms: manufacturers of consumer goods, producers of interme-
diate goods, ...
Downstream firms: distributors, retailers, ...

The market between upstream firms and downstream firms: the middle market
(or the wholesale market).

The market between downwtream firms and final consumers: the end market
(or the retail market).

Marc Bourreau adapted (TPT) Vertical relations 6 / 56

 Vertical relations and vertical restraints

Vertical integration

Vertical integration
A firm is vertically integrated when she controls over several or all of the
production steps involved in the creation of its product or service.

Marc Bourreau adapted (TPT) Vertical relations 7 / 56

 Vertical relations and vertical restraints

Vertical integration

Vertical integration
A firm is vertically integrated when she controls over several or all of the
production steps involved in the creation of its product or service.

Example: in the oil industry, the major companies carry out in-house the
following steps of oil production:
Exploration
Drilling
Refining
Distribution

→ In general, does a firm need to vertically integrate or not?

Marc Bourreau adapted (TPT) Vertical relations 7 / 56

 Vertical relations and vertical restraints

Vertical integration

To integrate or not to integrate an activity?

Marc Bourreau adapted (TPT) Vertical relations 8 / 56

 Vertical relations and vertical restraints

Vertical integration

To integrate or not to integrate an activity? → compare the cost (inluding the

opportunity cost)
of an internal production (vertical integration)
of having recourse to external firms (”to the market”)

→ Coase (1937) theory of “transaction costs” (transaction cost in the market

versus costs of organizing additional transactions within the firm)

Other factors:
ensuring the access to an essential input
internalizing some externalities
escaping regulation
...

Marc Bourreau adapted (TPT) Vertical relations 8 / 56

 Vertical relations and vertical restraints

Vertical integration
Why firms remain vertically integrated? → Also because they have invested
in some assets which are specific to the vertical relation.
This assets cannot be recycled without incurring costs in another transac-
tion
Profits from these investments disappear in case of a definitive breakdown
of the relation.

Marc Bourreau adapted (TPT) Vertical relations 9 / 56

 Vertical relations and vertical restraints

Vertical integration
Why firms remain vertically integrated? → Also because they have invested
in some assets which are specific to the vertical relation.
This assets cannot be recycled without incurring costs in another transac-
tion
Profits from these investments disappear in case of a definitive breakdown
of the relation.

Some examples of specific investments:

Specific to the location (ex: manufacturers of cans close to canning factories,
cement works close to cement warehouses)
Specific to the assets (ex: an aluminium plant invests in a refinery con-
ceived to process a bauxite ore of a precise quality).
Dedicated assets (investments specific to one client, for ex, special mold
for a perfume)
Specificities of human resource (ex: employees in a medical clinic trained
for the use of a specific software, etc.)
Marc Bourreau adapted (TPT) Vertical relations 9 / 56
 Vertical relations and vertical restraints

The hold-up problem

Notion of quasi-rent
Amount that one of the parties can require to the other during the negociation,
knowing that breaking up the negociation would not be profitable to the latter.

Marc Bourreau adapted (TPT) Vertical relations 10 / 56

 Vertical relations and vertical restraints

The hold-up problem

Notion of quasi-rent
Amount that one of the parties can require to the other during the negociation,
knowing that breaking up the negociation would not be profitable to the latter.

Example :
Firm A invests in a specific component for firm B, with a price which is
specified beforehand: profit Π1 for A. If B changes his mind, A makes Π2
on the market. Quasi-rent Π1 − Π2 > 0.
The hold-up problem: if Π1 − Π2 > 0, B can improve her situation by
holding-up A and keeping the quasi-rent (A is expropriated of a part of
its profit from the investment). If A anticipates, she will not invest in the
asset specific to the relation.
The contract negociations become complex
Under-investment in assets specific to the relation
Renegociations are frequent and transaction costs are high.
→ A vertical integration verticale can be a solution.
Marc Bourreau adapted (TPT) Vertical relations 10 / 56
 Vertical relations and vertical restraints

Vertical integration

But vertical integration is a radical solution.

Lots of the benefits from a vertical integration can be achieved by long-term

contract between firms:
Joint ventures
Outsourcing
Franchise
Exclusivity
...

→ Vertical restraints

Marc Bourreau adapted (TPT) Vertical relations 11 / 56

 Vertical relations and vertical restraints

Vertical restraints

Vertical restraints
Contractual terms between firms in a client-supplier relationship, which goes
beyond simple pricing rules and restrain what the other can do

Marc Bourreau adapted (TPT) Vertical relations 12 / 56

 Vertical relations and vertical restraints

Vertical restraints

Vertical restraints
Contractual terms between firms in a client-supplier relationship, which goes
beyond simple pricing rules and restrain what the other can do

Vertical restraints in pricing :

Minimum resale price maintenance (RPM)...
Franchise (two-part tariffs)

Vertical restraints non-tariff :

Exclusive territory
Selective distribution
Minimum amount on quantities to be traded
...

Marc Bourreau adapted (TPT) Vertical relations 12 / 56

 Vertical relations and vertical restraints

Vertical restraints

Definition of vertical restraints by the European Commission (Guidelines on

vertical restraints):

“Vertical restraints are agreements or concerted practices entered into

between two or more companies each of which operates, for the purposes of
the agreement, at a different level of the production or distribution chain, and
relating to the conditions under which the parties may purchase, sell or resell
certain goods or services.”

Marc Bourreau adapted (TPT) Vertical relations 13 / 56

 Vertical relations and vertical restraints

Vertical restraints

Why firms use vertical restraints?

For efficiency issues:

To solve the problem of double marginalization
To avoid free-rider problem from downstream firms
To price discriminate

For anti-competitive incentives:

To control competition
Establish entry barriers

Marc Bourreau adapted (TPT) Vertical relations 14 / 56

 The double marginalization problem

The double marginalization problem

The double marginalization problem or the problem of vertical externality

(Spengler 1950).

We consider an upstream firm (ex: a manufacturer) and a donwstream one (ex:

a retailer).

General idea
If the manufacturer and the retailer both have market power, each of them will
set a price higher than the cost (strictly positive margin), which will lead to a
price too high in the value chain

“What is worse than a monopoly? A chain of monopolies!”

Marc Bourreau adapted (TPT) Vertical relations 15 / 56

 The double marginalization problem

A model

Upstream firm U produces an intermediate good in monopoly

She sells this good to a retailer D in monopoly which commercializes the
good to final consumers
The final demand function is given by Q = D(p) = a − p
The marginal cost of the manufacturer is c and c < a
The marginal cost of the retailer is cD
We note w the wholesale price set by the firm U

Marc Bourreau adapted (TPT) Vertical relations 16 / 56

 The double marginalization problem

A model

Upstream firm U produces an intermediate good in monopoly

She sells this good to a retailer D in monopoly which commercializes the
good to final consumers
The final demand function is given by Q = D(p) = a − p
The marginal cost of the manufacturer is c and c < a
The marginal cost of the retailer is cD
We note w the wholesale price set by the firm U
Thus the “perceived marginal cost” of the retailer D is w + cD
We assume that cD = 0

A two-stage game:
1 U sets the wholesale price w
2 D sets the retail price p

Marc Bourreau adapted (TPT) Vertical relations 16 / 56

 The double marginalization problem

A model

We are going to compare the two situations:

Separate firms Vertically integrated firms

Marc Bourreau adapted (TPT) Vertical relations 17 / 56

 The double marginalization problem

Case of separate firms

Problem of the downstream firm (the retailer)

maxΠD = p − w a − p .



p

Marc Bourreau adapted (TPT) Vertical relations 18 / 56

 The double marginalization problem

Case of separate firms

Problem of the downstream firm (the retailer)

maxΠD = p − w a − p .



p

The first order condition is

∂ΠD a+w
= 0 ⇐⇒ p = .
∂p 2

Marc Bourreau adapted (TPT) Vertical relations 18 / 56

 The double marginalization problem

Case of separate firms

Problem of the downstream firm (the retailer)

maxΠD = p − w a − p .



p

The first order condition is

∂ΠD a+w
= 0 ⇐⇒ p = .
∂p 2

The demand function for the final product, that is, for the intermediate good,
is
a−w
q=a−p=
2

Marc Bourreau adapted (TPT) Vertical relations 18 / 56

 The double marginalization problem

Case of separate firms

The manufacturer anticipates the retailer’s pricing. We then have:

Producer’s problem
a−w
 
maxΠU = (w − c)q(w) = (w − c) .
w 2

Marc Bourreau adapted (TPT) Vertical relations 19 / 56

 The double marginalization problem

Case of separate firms

The manufacturer anticipates the retailer’s pricing. We then have:

Producer’s problem
a−w
 
maxΠU = (w − c)q(w) = (w − c) .
w 2

The first order condition of the problem is

∂ΠU a+c
= 0 ⇐⇒ w = .
∂w 2

Marc Bourreau adapted (TPT) Vertical relations 19 / 56

 The double marginalization problem

Case of separate firms

By replacing w with its value, we find the retail price in equilibrium:

3a + c
p= .
4

Marc Bourreau adapted (TPT) Vertical relations 20 / 56

 The double marginalization problem

Case of separate firms

By replacing w with its value, we find the retail price in equilibrium:

3a + c
p= .
4

The total surplus of the firms are:

(a − c)2 (a − c)2 3 (a − c)2

SP = ΠD + ΠU = + = .
16 8 16

Marc Bourreau adapted (TPT) Vertical relations 20 / 56

 The double marginalization problem

Vertical integration

We assume that firm U and firm D are vertically integrated.

Then it becomes the classical monopoly problem:

maxΠIV = p − c a − p ,



pIV

Marc Bourreau adapted (TPT) Vertical relations 21 / 56

 The double marginalization problem

Vertical integration

We assume that firm U and firm D are vertically integrated.

Then it becomes the classical monopoly problem:

maxΠIV = p − c a − p ,



pIV

We find
a+c a−c
pIV = et qIV = ,
2 2
and
(a − c)2
SPIV = ΠIV = .
4

Marc Bourreau adapted (TPT) Vertical relations 21 / 56

 The double marginalization problem

Comparizon

We have:
p > pIV
and
SP < SPIV ,

Which means that:

i. Consumer surplus is higher when there is vertical integration,
ii. Firms surplus is higher when there is vertical integration.

We call it the problem of double marginalization.

Marc Bourreau adapted (TPT) Vertical relations 22 / 56

 The double marginalization problem

Alternative solutions to integration

The problem of double marginalization: an argument for vertical integration?

Marc Bourreau adapted (TPT) Vertical relations 23 / 56

 The double marginalization problem

Alternative solutions to integration

The problem of double marginalization: an argument for vertical integration?

No, there are other alternative solutions → vertical restraints.

Marc Bourreau adapted (TPT) Vertical relations 23 / 56

 The double marginalization problem

Alternative solutions to integration

The problem of double marginalization: an argument for vertical integration?

No, there are other alternative solutions → vertical restraints.

An upstream firm could prefer these alternatives:

Costs to manage employees of the distribution channel
Distant geographical market for the producer and the distributor
...

Marc Bourreau adapted (TPT) Vertical relations 23 / 56

 The double marginalization problem

Two part tariff

Let’s consider an upstream firm (U) that proposes a two-part pricing to the
downstream firm (D)

Marc Bourreau adapted (TPT) Vertical relations 24 / 56

 The double marginalization problem

Two part tariff

Let’s consider an upstream firm (U) that proposes a two-part pricing to the
downstream firm (D)
The price: a per-unit price (w) and a fixed part (F)

Marc Bourreau adapted (TPT) Vertical relations 24 / 56

 The double marginalization problem

Two part tariff

Let’s consider an upstream firm (U) that proposes a two-part pricing to the
downstream firm (D)
The price: a per-unit price (w) and a fixed part (F)
Firm U sets the unit price (w) at marginal cost: w = c

Marc Bourreau adapted (TPT) Vertical relations 24 / 56

 The double marginalization problem

Two part tariff

Let’s consider an upstream firm (U) that proposes a two-part pricing to the
downstream firm (D)
The price: a per-unit price (w) and a fixed part (F)
Firm U sets the unit price (w) at marginal cost: w = c
Then the problem of firm D is:

maxΠD = p − c a − p − F



p

Marc Bourreau adapted (TPT) Vertical relations 24 / 56

 The double marginalization problem

Two part tariff

Let’s consider an upstream firm (U) that proposes a two-part pricing to the
downstream firm (D)
The price: a per-unit price (w) and a fixed part (F)
Firm U sets the unit price (w) at marginal cost: w = c
Then the problem of firm D is:

maxΠD = p − c a − p − F



p

It is the monopoly profit minus the fixed cost F !

Marc Bourreau adapted (TPT) Vertical relations 24 / 56

 The double marginalization problem

Tarification en deux parties

Therefore we have
a+c a−c
p= = pIV et q = = qIV .
2 2

The profits of the two firms are

(a − c)2
ΠD = − F and ΠU = F
4
The total profit of firms is maximal and equal to ΠIV .

The allocation of the total profit depends on F.

Marc Bourreau adapted (TPT) Vertical relations 25 / 56

 The double marginalization problem

Two-part tariff

Conclusion
If non-linear contracts are possible then the optimal solution under vertical
separation is identical to that under vertical integration.

→ Vertical restraint (non linear pricing contract) allows to lower the final price,
which is beneficial to consumers.

Limit
If there is competition between retailers, a fixed tariff is not sufficient to
capture the whole monopoly profit

Marc Bourreau adapted (TPT) Vertical relations 26 / 56

 The double marginalization problem

Other alternative: maximum retail price (price ceiling)

The producer can also set a maximum resale price (or a sales quota).

Marc Bourreau adapted (TPT) Vertical relations 27 / 56

 The double marginalization problem

Other alternative: maximum retail price (price ceiling)

The producer can also set a maximum resale price (or a sales quota).

If firm U sets a maximum retail price equal to pIV , firm D sets its retail price...
at the authorized maximum price.

Marc Bourreau adapted (TPT) Vertical relations 27 / 56

 The double marginalization problem

Other alternative: maximum retail price (price ceiling)

The producer can also set a maximum resale price (or a sales quota).

If firm U sets a maximum retail price equal to pIV , firm D sets its retail price...
at the authorized maximum price.

Then, the share of surplus between the upstream and the downstream firm is
defined by the wholesale price w:

If the upstream firm has all the market power, she sets
a+c
w = pIV =
2
If the downstream firm has all the market power, the upstream firm (U)
sets w = c

Marc Bourreau adapted (TPT) Vertical relations 27 / 56

 The double marginalization problem

An example

Blockbuster’s solution
Before 1998, in the US, video distributors were selling videocassette to
videostores at a fixed price of from approximately $ 65 to 70
The videostore then decided the quantity of cassettes and the rental price
If it had a market power: problem of double marginalization
Blockbuster introduced a new type of contracts: sharing of the income at
a rate of 40 to 60% and a fixed price of $ 8
Mortimer estimated this new type of contract (adopted by the others) led
to:
A decrease of the rental price of $ 4.64 to $ 4.08 in average
An increase of the number of cassettes

Marc Bourreau adapted (TPT) Vertical relations 28 / 56

 The free-riding problem

The free-riding problem

... or problem of incentives to increase the sales effort.

There can be horizontal externalities between distributors and retailers, which

can lead to a free-riding problem (”passager clandestin” in French).

Externalities on the quality and the level of service proposed by the retailer:
Advertisement by the retailer
Presence and training of commercial adviser
Service quality
Showrooms

If services are public goods, there is very weak incentives to provide them.

Marc Bourreau adapted (TPT) Vertical relations 29 / 56

 The free-riding problem

Some examples

The development of Internet as a merchandizing channel raises several prob-

lems of free-riding.

Free-riding between retailers

A consumer can take advantage of some advise at Fnac
then buy the product at an online discounter

Free-riding between the distributor and the retailer

Fear of retailers that distributors can also sell their product on the Internet
by themselves
However if free-riding is a problem, the distributor is well-advised to
avoid it, so he would rather not lower the price

Marc Bourreau adapted (TPT) Vertical relations 30 / 56

 The free-riding problem

Some examples

Carlton et Chevalier (2001) analysis on perfume and DVD industries.

Case of perfume
Perfume brands avoid selling their product on websites that suggest dis-
counts
or limit online sales on their own website (at high price)

Case of DVD
Sony and RCA had sold their DVD at a higher price of about 5% than their
authorized retailers
Distributors try to limit the availability of their products on non-authorized
retailers

Marc Bourreau adapted (TPT) Vertical relations 31 / 56

 The free-riding problem

The free-riding problem

We consider for instance an upstream producer (U)

Two dowstream retailers: D1 and D2
Each retailer has to choose the level of effort it will make in commercial
services: ei
Retailers then compete in prices (Bertrand competition)
Upstream and downstream marginal costs are normalized at 0

Impact of the commercial efforts on the perceived quality

Commercial efforts increase with the perceived quality:

s = s + e.

with e = e1 + e2 (commercial effort as a public good).

Marc Bourreau adapted (TPT) Vertical relations 32 / 56

 The free-riding problem

The free-riding problem

Marc Bourreau adapted (TPT) Vertical relations 33 / 56

 The free-riding problem

The free-riding problem

For a retailer, making a commercial effort is costly.

Let’s assume that the total cost of the retailer i is written:

µe2i
C q, ei = wq +


,
2
with µ > 1.

Marc Bourreau adapted (TPT) Vertical relations 34 / 56

 The free-riding problem

The free-riding problem

For a retailer, making a commercial effort is costly.

Let’s assume that the total cost of the retailer i is written:

µe2i
C q, ei = wq +


,
2
with µ > 1.

Consumer demand function is:

q = (a + s) − p = (a + e) − p,
assuming that s = 0.

Marc Bourreau adapted (TPT) Vertical relations 34 / 56

 The free-riding problem

Case of separate firms

Equilibrium in the end market

We have p1 = p2 = w et e1 = e2 = 0.

→ retailers cannot set a price above w (Bertrand), thus cannot recover the cost
of commercial effort ei > 0

The problem of the producer

The producer anticipates the equilibrium in the end market
He maximizes its profit

maxΠU = (w − c) (a − w) ,
w

Thus we have
a+c
w= .
2

Marc Bourreau adapted (TPT) Vertical relations 35 / 56

 The free-riding problem

Case of separate firms

In equilibrium, the producer surplus, the consumer surplus and the welfare
are:
(a − c)2
SP = ,
4
Z a
(a − c)2
SC = (a − x) dx = ,
w 8
3 (a − c)2
W= .
8

Marc Bourreau adapted (TPT) Vertical relations 36 / 56

 The free-riding problem

Vertical integration

Problem of a vertically integrated structure

If U and D are vertically integrated, the integration problem is:

µe2 µe2
maxΠIV = p − c a + e1 + e2 − p − 1 − 2


p,e1 ,e2 2 2

Marc Bourreau adapted (TPT) Vertical relations 37 / 56

 The free-riding problem

Vertical integration

Problem of a vertically integrated structure

If U and D are vertically integrated, the integration problem is:

µe2 µe2
maxΠIV = p − c a + e1 + e2 − p − 1 − 2


p,e1 ,e2 2 2

We have three first order conditions:

∂ΠIV
= 0 ⇒ a + e1 + e2 − 2p + c = 0,
∂p

∂ΠIV
= 0 ⇒ p − c − µe1 = 0,
∂e1
∂ΠIV
= 0 ⇒ p − c − µe2 = 0.
∂e2

Marc Bourreau adapted (TPT) Vertical relations 37 / 56

 The free-riding problem

Vertical integration

Solving the three first order conditions give the equilibrium price and the
optimal offort:

µ (a + c) − 2c
pIV =
2 µ−1

(a − c)
e1 = e2 = eIV =
2 µ−1

We have:

µ (a − c)2 µ2 (a − c)2 µ 3µ − 2 (a − c)2

SPIV = ΠIV =
, SCIV =
2 , et W = .
4 µ−1

2
8 µ−1 8 µ−1

Marc Bourreau adapted (TPT) Vertical relations 38 / 56

 The free-riding problem

Vertical integration

Firms surplus are higher with vertical integration,

SPIV > SP

and the global welfare also

WIV > W
even if prices are higher with vertical integration

pIV > p

Marc Bourreau adapted (TPT) Vertical relations 39 / 56

 The free-riding problem

Alternatives to vertical integration

Without vertical integration, can we fix this “horizontal externality” problem

between retailers (problem of incentives to commmercial effort)?

Marc Bourreau adapted (TPT) Vertical relations 40 / 56

 The free-riding problem

Alternatives to vertical integration

Without vertical integration, can we fix this “horizontal externality” problem

between retailers (problem of incentives to commmercial effort)?

The upstream firm should take some measures to reduce competition in the
downstream market.

Marc Bourreau adapted (TPT) Vertical relations 40 / 56

 The free-riding problem

Alternatives to vertical integration

Without vertical integration, can we fix this “horizontal externality” problem

between retailers (problem of incentives to commmercial effort)?

The upstream firm should take some measures to reduce competition in the
downstream market.
Exclusive territories
Resale price maintenance

Marc Bourreau adapted (TPT) Vertical relations 40 / 56

 The free-riding problem

Exclusive geographical area

Each retailers serves an exclusive geographical area.

However, such vertical restraint is not enough. We add a fixed franchising fee
F.

Let’s solve the equilibrium

Perceived quality depends on the sum of efforts of the two retailers
Exclusive territory agreement = each retailer serves half of the demand
The problem of the retailer (on an exclusive territory) is

a + e1 + e2 − pi µe2


maxΠD = pi − c − i − F.
pi ,ei 2 2

Marc Bourreau adapted (TPT) Vertical relations 41 / 56

 The free-riding problem

Exclusive geographical area

First order conditions

First order conditions are:
∂Π pi − c
=0⇒ − µei = 0
∂ei 2

∂Π a+e+c
= 0 ⇒ a + ei + ej − 2pi + c = 0 ⇒ pi =
∂pi 2

Conclusions
For the same level of effort, same price as in the case of vertical integration
But the commercial efforts are lowser
Thus exclusive geographical agreement improves the incentives to provide
services, but does not bring to a situation as efficient as vertical integration.

Marc Bourreau adapted (TPT) Vertical relations 42 / 56

 The free-riding problem

Resale price maintenance

Let’s assume that the producer sets the resale price of the retailer: it is a vertical
restraint called “resale price maintenance” (RPM).

This way, the producer can limit the competition intensity between retailers.

Marc Bourreau adapted (TPT) Vertical relations 43 / 56

 The free-riding problem

Resale price maintenance

Let’s assume that the producer sets the resale price of the retailer: it is a vertical
restraint called “resale price maintenance” (RPM).

This way, the producer can limit the competition intensity between retailers.

Assumptions
Retailers are forced to set a retail price of pIV
The wholesale price is T(q) = wq + F, with w < c

Problem of the retailer i

a + e1 + e2 − pIV µe2


maxΠD = pIV − w − i − F.
ei 2 2

Marc Bourreau adapted (TPT) Vertical relations 43 / 56

 The free-riding problem

Resale price maintenance

First order condition for the retailer i

∂Π pIV − w pIV − w
=0⇒ − µei = 0 ⇒ ei =
∂ei 2 2µ

For an optimal level of effort, the producer should set w such as that

pIV − w (a − c)
ei = =
2 µ−1


2µ

By replacing pIV with its expression, we find the wholesale price

3µ − 2c − µa
w=
< c.
2 µ−1

Marc Bourreau adapted (TPT) Vertical relations 44 / 56

 The free-riding problem

Resale price maintenance

The producer sets a unit price below its cost (w < c)

Setting the price at marginal cost (w = c) is not enough to encourage the
retailers to make optimal efforts
This is because they only take account the result of the effort on their own
profit and not on the rival firm (horizontal externality)
Setting a lower wholesale price increases the incentives to make an effort
in service quality
The fixed part of the wholesale price, F, may be used to redistribute the
profits

Marc Bourreau adapted (TPT) Vertical relations 45 / 56

 The free-riding problem

Resale price maintenance

In practice, resale price maintenance (RPM) is forbidden in many countries:

In Canada since 1951.
In the United Kingdom, since 1965.
In the United States, since 1976.

Nevertheless, it had been widely used by firms before it became illegal.

For instance, in UK, 44% of consumer expenses concerned goods sold by a RPM
type contract.

Today, it is legal to set a “suggested” price.

Marc Bourreau adapted (TPT) Vertical relations 46 / 56

 Competition between producers

Competition between producers

Definition
It is about competition between producers (or intra-brand competition) when
producers selling products to retailers (or to distributors) compete with each
other.

Marc Bourreau adapted (TPT) Vertical relations 47 / 56

 Competition between producers

Competition between producers

Market power of retailers

Let’s assume that retailers have market power.
Then uptstream firms should set a high wholesale unit price and a low
fixed part.
But the opportunity cost to sell a brand or another is different.
So the fixed part of the price can be a negative: ”slotting allowances”.

Marc Bourreau adapted (TPT) Vertical relations 48 / 56

 Competition between producers

Competition between producers

Market power of retailers

Let’s assume that retailers have market power.
Then uptstream firms should set a high wholesale unit price and a low
fixed part.
But the opportunity cost to sell a brand or another is different.
So the fixed part of the price can be a negative: ”slotting allowances”.

Externalities
There can be also externalities between producers.
For instance, an automobile manufacturer can train its sellers: with a
specific training and generic training.
Externality problem / free-riding: exclusive distribution?

Marc Bourreau adapted (TPT) Vertical relations 48 / 56

 Competition between producers

Competition between producers

Foreclosure
An exclusive distribution agreement can increase efficiency.
It can also increase market power (ex: agreement between Coca-Cola and
PepsiCo)

Marc Bourreau adapted (TPT) Vertical relations 49 / 56

 Competition between producers

Competition between producers

Foreclosure
An exclusive distribution agreement can increase efficiency.
It can also increase market power (ex: agreement between Coca-Cola and
PepsiCo)

Do vertical restraints stimulate collusion?

Vertical restraints can make collusion between producers easier.
Indeed, wholesale price may be difficult to observe.
Therefore, deviations are detected through the variation of retail price.
But other factors can also explain the price variation.
Vertical restraints on price can eliminate these variations.

Marc Bourreau adapted (TPT) Vertical relations 49 / 56

 Public policy

Public policy

Analysis of vertical restraints in terms of public policy is complex due to the

fact that some clauses can both have positive and negative effects on efficiency.

There are significant variations in public policy over time and between different
jurisdictions.

In the United States:

In 1967, the Supreme Court declares that vertical restraints is unlawful per
se.
In 1977, she ruled that non-tariff vertical restraints must be judged under
the Rule of Reason.
Since then, the rules tend to be softened. For instance, in 1997, maximum
price maintenance is judged legal.

Marc Bourreau adapted (TPT) Vertical relations 50 / 56

 Public policy

Public policy

In Europe:
The article 85(1) forbids vertical restraints
However, the article 85(3) grants certain exemptions when it is justified by
a valid technical or economic reasons or if consumers receives a fair part
of the benefice.
In 1967, exemption for exclusive territories and exclusive distribution.
In 1988, exemption for franchise agreements.
RPM is illegal but ”suggested” minimum or maximum price are accepted.

Marc Bourreau adapted (TPT) Vertical relations 51 / 56

 Vertical oligopoly and vertical mergers

Vertical oligopoly and vertical mergers

Exclusionary effects of vertical mergers:

Input foreclosure: vertical integration may lead to higher input prices for
competitors.
Higher price may be due to vertically integrated firms not selling inputs
on the market or, at least, restricting their supply.
Vertical integration can be used as a tool to increase rival’s costs.
Lesson: Vertical integration may raise the costs of nonintegrated down-
stream rivals. A higher wholesale price may or may not lead to higher
retail prices.
Such mergers may not hurt consumers (since retail prices may fall) and
often are not profitable for the firms involved in the merger.

Marc Bourreau adapted (TPT) Vertical relations 52 / 56

 Vertical oligopoly and vertical mergers

Vertical oligopoly and vertical mergers

Coordinated effects of vertical mergers:

Vertical integration may improve the viability of collusion among compet-
ing firms.
Key reason for vertical integration facilitating collusion: Outlets effect.
Vertical integration by an upstream firm reduces the number of outlets
through which its rivals can sell when deviating. This reduces their profit
from cheating and thus facilitates collusion.
Counteracting: Punishment effect. If an upstream firm integrates with
a downstream firm these profits now become part of the merged entity.
The merged entity can expect to make more profits in the non-cooperative
punishment phase than the upstream firm would make alone

Marc Bourreau adapted (TPT) Vertical relations 53 / 56

 Vertical oligopoly and vertical mergers

Vertical oligopoly and vertical mergers

Coordinated effects of vertical mergers

Merged entity suffers less than a stand-alone upstream firm from a switch
from collusive to punishment phases.
The outlets effect outweighs the punishment effect so that the net effect of
a vertical merger is to facilitate collusion
Lesson: Downstream vertical integration reduces the number of outlets
through which upstream rivals can sell and thus reduces profits if deviating
from a collusive outcome. Vertical integration may then facilitate collusion.

Marc Bourreau adapted (TPT) Vertical relations 54 / 56

 Key points to remember

Key points to remember (1)

Vertical relations is about two firms that succeed in the value chain.

Marc Bourreau adapted (TPT) Vertical relations 55 / 56

 Key points to remember

Key points to remember (1)

Vertical relations is about two firms that succeed in the value chain.
Vertical restraints are clauses in sale contracts that limit the behavior of the
buyer.

Marc Bourreau adapted (TPT) Vertical relations 55 / 56

 Key points to remember

Key points to remember (1)

Vertical relations is about two firms that succeed in the value chain.
Vertical restraints are clauses in sale contracts that limit the behavior of the
buyer.
If a producer and a retailer have both market power, they will both set
prices above the costs, which leads to a price too high in the value chain
(problem of double marginalization, two monopolies in a value chain are
worse than one monopoly).

Marc Bourreau adapted (TPT) Vertical relations 55 / 56

 Key points to remember

Key points to remember (1)

Vertical relations is about two firms that succeed in the value chain.
Vertical restraints are clauses in sale contracts that limit the behavior of the
buyer.
If a producer and a retailer have both market power, they will both set
prices above the costs, which leads to a price too high in the value chain
(problem of double marginalization, two monopolies in a value chain are
worse than one monopoly).
The upstream firm does not necessarily resort to a vertical integration to
solve the double marginalization problem.

Marc Bourreau adapted (TPT) Vertical relations 55 / 56

 Key points to remember

Key points to remember (1)

Vertical relations is about two firms that succeed in the value chain.
Vertical restraints are clauses in sale contracts that limit the behavior of the
buyer.
If a producer and a retailer have both market power, they will both set
prices above the costs, which leads to a price too high in the value chain
(problem of double marginalization, two monopolies in a value chain are
worse than one monopoly).
The upstream firm does not necessarily resort to a vertical integration to
solve the double marginalization problem.
If non-linear contracts are possible then two-part tariff under vertical sep-
aration is identical to the result of a vertical integration, which solves the
double marginalization problem.

Marc Bourreau adapted (TPT) Vertical relations 55 / 56

 Key points to remember

Key points to remember (2)

Horizontal externalities between producers and retailers may exist, which

may cause a ”free-riding” problem (For instance, if the retailer decides by
itself the effort he will put in product marketing, he doesn’t necessarily
have the incentives to do it).

Marc Bourreau adapted (TPT) Vertical relations 56 / 56

 Key points to remember

Key points to remember (2)

Horizontal externalities between producers and retailers may exist, which

may cause a ”free-riding” problem (For instance, if the retailer decides by
itself the effort he will put in product marketing, he doesn’t necessarily
have the incentives to do it).
In order to alleviate the free-riding problem, the upstream firm should
take some measures to reduce competition in the downstream market
(exclusive territories, resale maintenance).

Marc Bourreau adapted (TPT) Vertical relations 56 / 56

 Key points to remember

Key points to remember (2)

Horizontal externalities between producers and retailers may exist, which

may cause a ”free-riding” problem (For instance, if the retailer decides by
itself the effort he will put in product marketing, he doesn’t necessarily
have the incentives to do it).
In order to alleviate the free-riding problem, the upstream firm should
take some measures to reduce competition in the downstream market
(exclusive territories, resale maintenance).
Competition between upstream firms means that more than one producers
compete with each other to sell their products to retailers.

Marc Bourreau adapted (TPT) Vertical relations 56 / 56

 Key points to remember

Key points to remember (2)

Horizontal externalities between producers and retailers may exist, which

may cause a ”free-riding” problem (For instance, if the retailer decides by
itself the effort he will put in product marketing, he doesn’t necessarily
have the incentives to do it).
In order to alleviate the free-riding problem, the upstream firm should
take some measures to reduce competition in the downstream market
(exclusive territories, resale maintenance).
Competition between upstream firms means that more than one producers
compete with each other to sell their products to retailers.
Vertical restraints are prohibited by the article 85-1 of the treaty of Rome
but the article 85-3 grant exemptions when consumer benefits from the
restraint. Exclusive territory is exempted since 1967, franchise agreements
exempted since 1988. RPM is illegal but non-binding recommended prices
are allowed.

Marc Bourreau adapted (TPT) Vertical relations 56 / 56